Abstract

A fast multichannel Stokes/Mueller polarimeter with no mechanically moving parts has been designed to have close to optimal performance from 430 – 2000 nm by applying a genetic algorithm. Stokes (Mueller) polarimeters are characterized by their ability to analyze the full Stokes (Mueller) vector (matrix) of the incident light (sample). This ability is characterized by the condition number, κ, which directly influences the measurement noise in polarimetric measurements. Due to the spectral dependence of the retardance in birefringent materials, it is not trivial to design a polarimeter using dispersive components. We present here both a method to do this optimization using a genetic algorithm, as well as simulation results. Our results include fast, broad-band polarimeter designs for spectrographic use, based on 2 and 3 Ferroelectric Liquid Crystals, whose material properties are taken from measured values. The results promise to reduce the measurement noise significantly over previous designs, up to a factor of 4.5 for a Mueller polarimeter, in addition to extending the spectral range.

Figures (6)

(a) A Stokes polarimeter measures the polarization state of an arbitrary light source using a Polarization State Analyzer (PSA). (b) A Mueller polarimeter measures how the polarization state of light, generated by with a Polarization State Generator (PSG), is changed by a sample.

The four essential processes in a genetic algorithm are shown above. Sexual reproduction is performed by multi-point genetic crossover, giving rise to the next generation of individuals. Mutation can be simulated with simple bit negation (e.g. 0 → 1 and vice versa). Development is the process where a genotype is interpreted into its phenotype, i.e. the binary genome is interpreted as a polarimeter design. In the mating contest, one evaluates the fitness of each individual’s phenotype, and let the more fit individuals reproduce with higher probability than the less fit individuals.

Convergence of fitness as a function of generation number. μ and σ refer to the average and standard deviation of the population’s fitness, respectively. The best result from this simulation is the one shown in Fig. 4.

Condition number for two designs using 2 FLC retarders and 2 waveplates. By optimizing κ(λ) over a narrower part of the spectrum, we can design good polarimeters with fewer components. The polarimeter designs labeled “Visible” and “IR” show our two designs, optimized for 430 nm < λ < 1100 nm and 800 nm < λ < 1700 nm, respectively. For comparison with our “NIR” design, we show the previous simulated design from Ref. [30]. The curve labeled “Commercial” shows the measured condition number of a commercial instrument (MM16, Horiba, 2006) based on the same (FLC) technology.

Tables (3)

Table 2 Genetic Algorithm parameters. The “crossover rate” is the probability for two parents to undergo sexual reproduction (the alternative being asexual reproduction). The parameter “crossover points” refer to the number of points where we cut the genome during crossover (sexual reproduction). “Mutation rate” is the probability for any given individual to undergo one or several bit flip mutations in one generation

Metrics

Table 2

Genetic Algorithm parameters. The “crossover rate” is the probability for two parents to undergo sexual reproduction (the alternative being asexual reproduction). The parameter “crossover points” refer to the number of points where we cut the genome during crossover (sexual reproduction). “Mutation rate” is the probability for any given individual to undergo one or several bit flip mutations in one generation

Parameter

Value

Crossover rate

0.7

Crossover points

2

Mutation rate

0.2

Population size

500

Table 1

Orientation angles, θ, and normalized thicknesses L, of the components of the best 3-FLC polarimeter. (WP = (fixed) waveplate)

Tables (3)

Table 2

Genetic Algorithm parameters. The “crossover rate” is the probability for two parents to undergo sexual reproduction (the alternative being asexual reproduction). The parameter “crossover points” refer to the number of points where we cut the genome during crossover (sexual reproduction). “Mutation rate” is the probability for any given individual to undergo one or several bit flip mutations in one generation

Parameter

Value

Crossover rate

0.7

Crossover points

2

Mutation rate

0.2

Population size

500

Table 1

Orientation angles, θ, and normalized thicknesses L, of the components of the best 3-FLC polarimeter. (WP = (fixed) waveplate)